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Nilpotent centres via inverse integrating factors

Published online by Cambridge University Press:  23 March 2016

ANTONIO ALGABA ,
CRISTÓBAL GARCÍA  and
JAUME GINÉ
ANTONIO ALGABA
Affiliation:
Dept. Matemáticas, Facultad de Ciencias, University of Huelva, Huelva, Spain emails: algaba@uhu.es, cristoba@uhu.es
CRISTÓBAL GARCÍA
Affiliation:
Dept. Matemáticas, Facultad de Ciencias, University of Huelva, Huelva, Spain emails: algaba@uhu.es, cristoba@uhu.es
JAUME GINÉ
Affiliation:
Departament de Matemàtica, Escola Politècnica Superior, Universitat de Lleida, Av. Jaume II, 69, 25001, Lleida, Catalonia, Spain email: gine@matematica.udl.cat
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Abstract

In this paper, we are interested in the nilpotent centre problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centres. More general objects are considered as the formal inverse integrating factors. However, the existence of a formal inverse integrating factor is not sufficient to describe all the nilpotent centres. For the family studied in this paper, it is enough.

Keywords

non-linear differential systemsintegrability problemnilpotent centre problem
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 5 , October 2016 , pp. 781 - 795
Copyright
Copyright © Cambridge University Press 2016 

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